{"id":8414,"date":"2012-04-16T21:03:06","date_gmt":"2012-04-16T20:03:06","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8414"},"modified":"2021-12-30T01:23:28","modified_gmt":"2021-12-30T01:23:28","slug":"determine-o-conjunto-solucao-da-equacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8414","title":{"rendered":"Determine o conjunto solu\u00e7\u00e3o da equa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_8414' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8414' class='GTTabs_curr'><a  id=\"8414_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8414' ><a  id=\"8414_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8414'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determine o conjunto solu\u00e7\u00e3o da equa\u00e7\u00e3o $\\operatorname{sen} \\alpha\u00a0 &#8211; \\cos \\alpha\u00a0 = \\sqrt 2 $.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8414' onClick='GTTabs_show(1,8414)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8414'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Tendo em considera\u00e7\u00e3o que<\/p>\n<blockquote>\n<p>$$\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\beta } \\right) = \\operatorname{sen} \\alpha \\cos \\beta\u00a0 &#8211; \\cos \\alpha \\operatorname{sen} \\beta $$<\/p>\n<\/blockquote>\n<p>temos:<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{\\operatorname{sen} \\alpha\u00a0 &#8211; \\cos \\alpha\u00a0 = \\sqrt 2 }&amp; \\Leftrightarrow &amp;{\\operatorname{sen} \\alpha\u00a0 \\times \\frac{{\\sqrt 2 }}{2} &#8211; \\cos \\alpha\u00a0 \\times \\frac{{\\sqrt 2 }}{2} = \\sqrt 2\u00a0 \\times \\frac{{\\sqrt 2 }}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\operatorname{sen} \\alpha\u00a0 \\times \\cos \\frac{\\pi }{4} &#8211; \\cos \\alpha\u00a0 \\times \\operatorname{sen} \\frac{\\pi }{4} = 1} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\operatorname{sen} \\left( {\\alpha\u00a0 &#8211; \\frac{\\pi }{4}} \\right) = 1} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\alpha\u00a0 &#8211; \\frac{\\pi }{4} = \\frac{\\pi }{2} + 2k\\pi ,k \\in \\mathbb{Z}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\alpha\u00a0 = \\frac{{3\\pi }}{4} + 2k\\pi ,k \\in \\mathbb{Z}}<br \/>\n\\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8414' onClick='GTTabs_show(0,8414)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine o conjunto solu\u00e7\u00e3o da equa\u00e7\u00e3o $\\operatorname{sen} \\alpha\u00a0 &#8211; \\cos \\alpha\u00a0 = \\sqrt 2 $. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19666,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,302],"series":[],"class_list":["post-8414","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-equacoes-trigonometricas"],"views":2495,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat241.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8414","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8414"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8414\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8414"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}